The Cartesian monoid of partial piecewise shift operators is developed as a model for programming systems such as Backus’ FP. Special attention is paid to those elements which are equationally implicitly definable.

A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three parameters that are complex in the most general situation. The prop...

Descartes maintained that sensations of color and the like misrepresent the material world in normal circumstances. Some prominent scholars have argued that, to explain this Cartesian view, we must attribute to Descartes a causal account of sensory representation. I contend that neither the arguments motivating this reading nor the textual evidence offered in its support is sufficient to justif...